博雅讲座之一：Fractal Hardy space

讲座时间：2021年9月20日（周一）下午2:30-3:30

讲座人：董新汉教授，湖南师范大学

Abstract：The first singular, non-atomic, spectral measure was constructed by Jorgensen and Pedersen. They proved that 1/R-Cantor measure $\mu_R$ is a spectral measure with a spectrum $\Lambda$ if R is even. For any square integral function $f$, Let $F_{f,\Lambda}=\sum_{\lambda\in\Lambda}f^(\lambda)z^{\lambda}$. Hence, $H={F_{f, \Lambda}: f a is square integral function}$ is a complete subspace of Hardy space. In this talk, we mainly investigated the following problems: (1) Integral representation theorem of H; (2) Growth theorem of H；(3) Strichartz’s exceptional set and Carleson’s exceptional set under certain conditions; (4) Picard property, Cantor boundary behaviour of $F_{f,\Lambda}$, under Hadamard gap condition.

链接：/info/1206/25964.htm